In any \( \triangle A B C \), prove that \[a^{3} \sin (B-C)+b^{3} \sin (C-A)+c^{3} \sin (A-B)=0\]

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In any \( \triangle A B C \), prove that
\[a^{3} \sin (B-C)+b^{3} \sin (C-A)+c^{3} \sin (A-B)=0\]
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